How to have 2 windows display different modes in the 3D Viewport
Sure you can do that! I do it all the time.
When you drag out a new window, simply hold down Shift, at the same time, and that will tear that window away from the main interface! You can then move that new window to your other monitor and set it to what you like.
To change it to what you like, simply select this icon here:
Example